If ellipsoid height h and geoid height N are known, how is orthometric height H computed?

If ellipsoid height h and geoid height N are known, how is orthometric height H computed?

• A. H = h + N
• B. H = h - N
• C. H = N - h
• D. H = h * N

Answer: (B)

The key idea is how the heights relate to the geoid and the ellipsoid. Ellipsoidal height h is the distance above the reference ellipsoid, while orthometric height H is the distance above the geoid. The geoid height N, also called geoid undulation, represents the separation between the ellipsoid and the geoid, defined as N = h − H. Rearranging gives H = h − N. So if you know the ellipsoidal height and the geoid height, subtract the geoid height from the ellipsoidal height to get the orthometric height. For example, if h = 100 m and N = 30 m, then H = 70 m. If N is negative, subtracting a negative increases H accordingly. The other options don’t reflect the standard relationship between these three quantities: adding N, taking N minus h, or multiplying do not correspond to how ellipsoidal height, geoid height, and orthometric height are defined and related.

The key idea is how the heights relate to the geoid and the ellipsoid. Ellipsoidal height h is the distance above the reference ellipsoid, while orthometric height H is the distance above the geoid. The geoid height N, also called geoid undulation, represents the separation between the ellipsoid and the geoid, defined as N = h − H. Rearranging gives H = h − N.

So if you know the ellipsoidal height and the geoid height, subtract the geoid height from the ellipsoidal height to get the orthometric height. For example, if h = 100 m and N = 30 m, then H = 70 m. If N is negative, subtracting a negative increases H accordingly.

The other options don’t reflect the standard relationship between these three quantities: adding N, taking N minus h, or multiplying do not correspond to how ellipsoidal height, geoid height, and orthometric height are defined and related.